A note on generalized \(q\)-difference equations for \(q\)-beta and Andrews-Askey integral

DOI10.1016/j.jmaa.2013.11.027zbMath1308.39010OpenAlexW1971185117MaRDI QIDQ2019165

Jian Cao

Publication date: 27 March 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2013.11.027

zbMATH Keywords

generating function\(q\)-difference equationAndrews-Askey integral\(q\)-exponential operator\(q\)-Chu-Vandermonde formulaAl-Salam-Carlitz polynomialRamanujan's \(q\)-beta integral

Mathematics Subject Classification ID

Difference equations, scaling ((q)-differences) (39A13)

Related Items (14)

Homogeneous \(q\)-difference equations and generating functions for \(q\)-hypergeometric polynomials ⋮ Remarks on a generalizedq-difference equation ⋮ \(q\)-difference equation and \(q\)-polynomials ⋮ \(q\)-difference equations for Askey-Wilson type integrals via \(q\)-polynomials ⋮ Generalized q-Laguerre type polynomials and q-partial differential equations ⋮ Two \(q\)-operational equations and Hahn polynomials ⋮ A note on q-difference equations for Cigler’s polynomials ⋮ Some iterated fractional \(q\)-integrals and their applications ⋮ A note on \(q\)-difference equations for Ramanujan's integrals ⋮ Applications of a generalized \(q\)-difference equation ⋮ Homogeneous \(q\)-partial difference equations and some applications ⋮ A note on $q$-partial difference equations and some applications to generating functions and $q$-integrals ⋮ q-Laguerre polynomials and related q-partial differential equations ⋮ q-Difference equations for the generalized Cigler’s polynomials

Cites Work

• On Carlitz's trilinear generating functions
• Moments for generating functions of Al-Salam-Carlitz polynomials
• \(q\)-differential operator identities and applications
• The Cauchy operator for basic hypergeometric series
• Orthogonal polynomials and some q-beta integrals of Ramanujan
• q-beta integrals and the q-Hermite polynomials
• The \(q\)-harmonic oscillator and the Al-Salam and Carlitz polynomials
• Parameter augmentation for basic hypergeometric series. II
• Some operator identities and \(q\)-series transformation formulas
• Generating functions for certain q-orthogonal polynomials
• \(q\)-difference equation and the Cauchy operator identities
• A Note onq-Integrals and Certain Generating Functions
• Twoq-difference equations andq-operator identities
• An extension of the non-terminating₆φ₅summation and the Askey–Wilson polynomials
• ALTERNATIVE PROOFS OF GENERATING FUNCTIONS FOR HAHN POLYNOMIALS AND SOME APPLICATIONS
• Another q-Extension of the Beta Function
• Two Integrals of Ramanujan
• An Introduction to Ramanujan's "lost" Notebook
• The Pearson Equation and the Beta Integrals
• Complex Analysis: A Brief Tour into Higher Dimensions
• SOME APPLICATIONS OF q-DIFFERENTIAL OPERATOR
• Some Orthogonal q‐Polynomials
• Some polynomials related to theta functions
• On the \(q\)-polynomials: A distributional study
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